Question

the second polygon is a scaled copy of the first.
a. highlight one pair of corresponding points and two pairs of corresponding sides in the original polygon and its copy. consider using colored pencils to highlight corresponding sides.
b. what scale factor takes the original polygon to its smaller copy? explain or show your reasoning.

Explanation:

Step1: Select corresponding elements

Choose the top - left vertex of both polygons as a pair of corresponding points. For corresponding sides, choose the top - horizontal sides and the left - vertical sides of both polygons.

Step2: Determine scale factor

Count the number of grid units for a side of the original polygon and the corresponding side of the scaled - down polygon. Suppose a side of the original polygon is 6 grid units long and the corresponding side of the smaller polygon is 3 grid units long. The scale factor $k$ is given by the ratio of the length of a side of the smaller polygon to the length of the corresponding side of the original polygon. So, $k=\frac{3}{6}=\frac{1}{2}$.

Answer:

a. (Corresponding points and sides can be selected as described above)
b. The scale factor is $\frac{1}{2}$ because the ratio of the length of a side of the smaller polygon to the length of the corresponding side of the original polygon is $\frac{1}{2}$.